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JEE Main202131 Aug 2021Morning ShiftMathematicsVector AlgebraActual

Let a → and b → be two vectors such that | 2 a → + 3 b → | = | 3 a → + b → | and the angle between a → and b → is 60 ° . If 1 8 a → is a unit vector, then | b → | is equal to :

Options

  1. A8
  2. B4
  3. C6
  4. D5

Correct answer

D. 5

Step-by-step solution

Given that 1 8 a → is a unit vector. | a → | = 8 | 2 a → + 3 b → | 2 = | 3 a → + b → | 2 We know that a →   ·   b →     =   a →   b →   cos   θ   , ⇒ 4 | a → | 2 + 9 | b → | 2 + 12 | a → | | b → | cos 60 ° = 9 | a → | 2 + | b → | 2 + 6 | a → | | b → | cos 60 ° ⇒ 5 | a → | 2 = 8 | b → | 2 + 6 | a → | | | b → &#

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